Discrete MathLogic Sets Let A x is in Z x 6a 4 for some i

Discrete Math/Logic Sets

Let A = {x is in Z| x = 6a + 4 for some integer a}

Let B = {y is in Z| y = 18b - 2 for some integer b}

Let C = {z is in Z| z = 18c + 16 for some integer c}

Prove or disprove:

a) A is a subset of B

b) B is a subset of A

c) B = C

Solution

Let\'s revisit B and C ...
y = 6*3b - 2
z = 6*3c + 6*3 - 2

Thus, for any b, c=b-1 will make y=z.
They are the same set.

For A, let\'s substitute d = a+1, so that 6a+4 = 6z - 2
Combine that with the generator for set B: 6*3b - 2
Where z = 3b, the number will be in both sets.